anonymous
  • anonymous
***PLEASE HELP! WILL MEDAL***Express answer in exact form. Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
When the radius of the circle is 8" and chord length is also 8" Then this chord forms an equilateral triangle a the center . The angle subtended by the chord/arc at the center is also 60° or π/3 radians Area of the larger segment = Area of the circle − area of the smaller segment Area of the smaller segment = Area of the sector − area of the equilateral triangle formed by the chord at the center Area of a sector = ½ R² θ where θ is the angle in radians subtended by the arc at the center of the circle =½×8²×π/3=32π/3 inch ² Area of equilateral triangle of side 8 "=½×8×8sin60° =32×√3/2 =16√3 inch² Hence Area of the smaller segment = 32π/3 − 16√3 Area of the circle =πR²=π×8²=64π inch² Hence area of larger segment =Area of the circle − area of the smaller segment =64π−{32π/3 − 16√3}= 160π/3 + 16√3 inch²
anonymous
  • anonymous
Does that help?
anonymous
  • anonymous

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anonymous
  • anonymous
Woah
anonymous
  • anonymous
Give me a sec to read it all
anonymous
  • anonymous
Or Area = 64pi - (128pi^3-96root3)/6
anonymous
  • anonymous
omg
anonymous
  • anonymous
?
anonymous
  • anonymous
Did you get it right?
anonymous
  • anonymous
Yeah that's what I'm thinking
anonymous
  • anonymous
Ok your welcome :)
anonymous
  • anonymous
didn't really help, but okay
anonymous
  • anonymous
Whatever goodbye
Nurali
  • Nurali
Two radii and the chord all = 8" All three sides of the triangle so formed are equal. Each of the angles of an equilateral triangle = 60 Degree. Area of a pie piece (called a circle sector) = central angle over entire angle of a circle * r^2 Area of sector = 60/ 360 * pi * r^2 Area of sector = 1/6 * 3.14 * 8^2 Area of sector = 33.51 square inches. Now find the area of an equilateral Triangle. The area of a triangle is the base * height /2 The height = sqr(8^2 - 4^2) = sqr(48) = 6.928 The area of the triangle = 8*6.928/2 = 27.712 So the area of the smaller segment = area of the sector - area of the triangle small segment = 33.1 - 27.712 = 5.798 square inches.
anonymous
  • anonymous
It's fine. I'm just a little slow that's all. I've never been taught any of this before
anonymous
  • anonymous
I really can't help it @AnasAlazzawi

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